Stackelberg Location on a Tree Network with Fuzzy Random Quantities Demanded

This paper focuses on a new Stackelberg location problem on a tree network with demands whose quantities are given uncertainly and vaguely. By representing their quantities as fuzzy random variables on the tree network, the optimal location problem can be formulated as a fuzzy random programming problem for finding Stackelberg equilibrium. By using both their α-level sets for fuzziness and their satisfaction level for a given probability for randomness, it can be reformulated as a version of conventional Stackelberg location problem on the tree network. Theorems for its complexity are shown based upon the characteristics of the facility location.